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Date	May 2021	Marks available	1	Reference code	21M.1.SL.TZ2.7
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 2
Command term	Suggest	Question number	7	Adapted from	N/A

Question

A large school has students from Year 6 to Year 12.

A group of $80$ students in Year 12 were randomly selected and surveyed to find out how many hours per week they each spend doing homework. Their results are represented by the following cumulative frequency graph.

This same information is represented by the following table.

There are $320$ students in Year 12 at this school.

Find the median number of hours per week these Year 12 students spend doing homework.

[2]

Given that $10 %$ of these Year 12 students spend more than $k$ hours per week doing homework, find the value of $k$ .

[3]

Find the value of $p$ and the value of $q$ .

[4]

Estimate the number of Year 12 students that spend more than $15$ hours each week doing homework.

[3]

Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.

[1]

e.i.

Suggest a more appropriate sampling method.

[1]

e.ii.

Markscheme

evidence of median position (M1)

$40$ students

median $= 14$ (hours) A1

[2 marks]

recognizing there are $8$ students in the top $10 %$ (M1)

$72$ students spent less than $k$ hours (A1)

$k = 18$ (hours) A1

[3 marks]

$15$ hours is $60$ students OR $p = 60 - 4$ (M1)

$p = 56$ A1

$21$ hours is $76$ students OR $q = 80 - 76$ OR $q = 80 - 4 - 56 - 16$ (A1)

$q = 4$ A1

[4 marks]

$20$ of the $80$ students OR $\frac{1}{4}$ spend more than $15$ hours doing homework (A1)

$\frac{20}{80} = \frac{x}{320}$ OR $\frac{1}{4} \times 320$ OR $4 \times 20$ (A1)

$80$ (students) A1

[3 marks]

only year 12 students surveyed OR amount of homework might be different for different year levels R1

[1 mark]

e.i.

stratified sampling OR survey students in all years R1

[1 mark]

e.ii.

Examiners report

[N/A]

e.i.

[N/A]

e.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques

Show 29 related questions

EXM.1.SL.TZ0.2c:
Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.
EXM.2.SL.TZ0.1c:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1a:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1d.i:
Calculate Pearson’s product moment correlation coefficient, $r$ .
18M.1.SL.TZ1.S_2a:
Find the value of the interquartile range.
19M.2.SL.TZ1.S_3b:
The graph of $f$ has a horizontal tangent line at $x = 0$ and at $x = a$ . Find $a$ .
17M.2.SL.TZ1.S_1b.i:
Find the mean.
17M.2.SL.TZ2.S_8b.i:
Write down the coordinates of A.
17M.2.SL.TZ2.S_8c.i:
Find the coordinates of B.
EXM.2.SL.TZ0.1b.i:
Show that 3 students will be selected from grade 12.
EXM.2.SL.TZ0.1d.iii:
Explain why the value of $r$ makes it appropriate to find the equation of a regression line.
EXM.2.SL.TZ0.1b.ii:
Calculate the number of students in each grade in the sample.
EXM.1.SL.TZ0.2b:
Hence, show that a data set with only 5 numbers in it cannot have any outliers.
17M.2.SL.TZ2.S_8b.ii:
Write down the rate of change of $f$ at A.
EXM.2.SL.TZ0.1d.ii:
Interpret the meaning of the value of $r$ in the context of the principal’s concerns.
EXM.1.SL.TZ0.2a:
Recalling definitions, such as the Lower Quartile is the $\frac{{n + 1}}{4}th$ piece of data with the data placed in order, find an expression for the Interquartile Range.
17M.2.SL.TZ2.S_8a:
Find the value of $p$ .
17M.2.SL.TZ2.S_8d:
Let $R$ be the region enclosed by the graph of $f$ , the $x$ -axis, the line $x = b$ and the line $x = a$ . The region $R$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
17M.2.SL.TZ1.S_1a.ii:
Find the value of the range.
22M.2.SL.TZ2.5b:
Verify that the measurement of $0.46$ seconds is not an outlier.
17M.2.SL.TZ1.S_1a.i:
Write down the mode.
21M.1.SL.TZ1.4b:
Hence, find the minimum possible value of $L$ .
18M.1.SL.TZ1.S_2b:
One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.
17M.2.SL.TZ2.S_8c.ii:
Find the the rate of change of $f$ at B.
21M.1.SL.TZ2.7e.i:
Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.
EXM.2.SL.TZ0.1e:
Another student at the school, Jasmine, has a self-esteem value of 29.

By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.
21M.1.SL.TZ1.4a:
Find the minimum possible value of $U$ .
22M.1.SL.TZ1.3a:
Find the largest value of $c$ that would not be considered an outlier.
17M.2.SL.TZ1.S_1b.ii:
Find the variance.

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Topic 4—Statistics and probability

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